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Many-access channel (MnAC) model allows the number of users in the system andthe number of active users to scale as a function of the blocklength and assuch is suited for dynamic communication systems with massive number of userssuch as the Internet of Things. Existing MnAC models assume a priori knowledgeof channel gains which is impractical since acquiring Channel State Information(CSI) for massive number of users can overwhelm the available radio resources.This paper incorporates Rayleigh fading effects to the MnAC model and derivesan upper bound on the symmetric message-length capacity of the Rayleigh-fadingGaussian MnAC. Furthermore, a lower bound on the minimum number of channel usesfor discovering the active users is established. In addition, the performanceof Noisy Combinatorial Orthogonal Matching Pursuit (N-COMP) based group testing(GT) is studied as a practical strategy for active device discovery.Simulations show that, for a given SNR, as the number of users increase, therequired number of channel uses for N-COMP GT scales approximately the same wayas the lower bound on minimum user identification cost. Moreover, in the lowSNR regime, for sufficiently large population sizes, the number of channel usesrequired by N-COMP GT was observed to be within a factor of two of the lowerbound when the expected number of active users scales sub-linearly with thetotal population size.

Capacity Bounds and User Identification Costs in Rayleigh-Fading Many-Access Channel